Some remarks on the connectivity of Julia sets for 2-dimensional diffeomorphisms
| dc.creator | Dujardin, Romain | |
| dc.date | 2004-12-08 | |
| dc.date.accessioned | 2026-07-07T05:15:05Z | |
| dc.date.available | 2026-07-07T05:15:05Z | |
| dc.description | We explore the connected/disconnected dichotomy for the Julia set of polynomial automorphisms of C^2. We develop several aspects of the question, which was first studied by Bedford-Smillie. We introduce a new sufficient condition for the connectivity of the Julia set, that carries over for certain H{é}non-like and birational maps. We study the structure of disconnected Julia sets and the associated invariant currents. This provides a simple approach to some results of Bedford-Smillie, as well as some new corollaries --the connectedness locus is closed, construction of external rays in the general case, etc. We also prove the following theorem: a hyperbolic polynomial diffeomorphism of C^2 with connected Julia set must have attracting or repelling orbits. This is an analogue of a well known result in one dimensional dynamics. | |
| dc.identifier | https://arxiv.org/abs/math/0412162 | |
| dc.identifier | http://arxiv.org/abs/math/0412162 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73520 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Complex Variables | |
| dc.subject | 37Fxx | |
| dc.title | Some remarks on the connectivity of Julia sets for 2-dimensional diffeomorphisms | |
| dc.type | text |